use the image below for the questions 10-16. 10. how many sides does the polygon afdcb have? 11. is it concave or convex? 12. what is the length of $\overline{af}$? 13. what is the length of $\overline{ae}$? 14. what is the perimeter of triangle afe? 15. what is the area of triangle afe? 16. what is the perimeter of parallelogram aedc? image shows coordinate grid with points a(-4, 3), b(-1, 5), c(2, 3), d(4, -3), e(-2, -3), f(-4, -3)

Question

Accepted Answer

### Question 10: How many sides does the polygon AFDCB have?
# Explanation:
## Step1: Identify the vertices of the polygon AFDCB.
The vertices are A, F, D, C, B, and back to A. So we list the vertices: A, F, D, C, B.
## Step2: Count the number of vertices (which equals the number of sides in a polygon).
There are 5 vertices (A, F, D, C, B), so the number of sides is 5.
# Answer: 5

### Question 11: Is it concave or convex?
# Brief Explanations:
To determine if a polygon is concave or convex, we check the interior angles. A convex polygon has all interior angles less than 180 degrees, and a concave polygon has at least one interior angle greater than 180 degrees. Looking at the polygon AFDCB, all interior angles appear to be less than 180 degrees (visually, the polygon "bulges" outwards, no indentations).
# Answer: Convex

### Question 12: What is the length of $\overline{AF}$?
# Explanation:
## Step1: Identify the coordinates of A and F.
A is $(-4, 3)$ and F is $(-4, -3)$.
## Step2: Use the distance formula for vertical lines (since x - coordinates are the same).
The distance formula for vertical lines is $|y_2 - y_1|$. Here, $y_1 = 3$, $y_2 = -3$. So the length is $| - 3 - 3| = | - 6| = 6$.
# Answer: 6

### Question 13: What is the length of $\overline{AE}$?
# Explanation:
## Step1: Identify the coordinates of A and E.
A is $(-4, 3)$ and E is $(-2, -3)$.
## Step2: Use the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
Here, $x_1 = -4$, $y_1 = 3$, $x_2 = -2$, $y_2 = -3$. So $d = \sqrt{(-2 - (-4))^2 + (-3 - 3)^2} = \sqrt{(2)^2 + (-6)^2} = \sqrt{4 + 36} = \sqrt{40} = 2\sqrt{10}$ (or approximately 6.32). But if we consider the grid, maybe we can calculate the horizontal and vertical distances. Horizontal distance: $-2 - (-4) = 2$, vertical distance: $-3 - 3 = -6$. Then using Pythagoras: $2^2 + 6^2 = 4 + 36 = 40$, so $\sqrt{40} = 2\sqrt{10}$.
# Answer: $2\sqrt{10}$ (or approximately 6.32)

### Question 14: What is the perimeter of triangle AFE?
# Explanation:
## Step1: Find the lengths of AF, FE, and AE.
- Length of AF: From question 12, AF = 6.
- Length of FE: Coordinates of F(-4, -3) and E(-2, -3). Horizontal line, so length is $| - 2 - (-4)| = 2$.
- Length of AE: From question 13, AE = $2\sqrt{10}$ (or approximately 6.32).
## Step2: Sum the lengths.
Perimeter = AF + FE + AE = $6 + 2 + 2\sqrt{10} = 8 + 2\sqrt{10}$ (or approximately $8 + 6.32 = 14.32$).
# Answer: $8 + 2\sqrt{10}$ (or approximately 14.32)

### Question 15: What is the area of triangle AFE?
# Explanation:
## Step1: Identify the base and height.
For triangle AFE, we can take FE as the base (length 2, from question 14) and the vertical distance from A to the line FE as the height. The y - coordinate of FE is -3, and the y - coordinate of A is 3, so the height is $|3 - (-3)| = 6$.
## Step2: Use the area formula for a triangle $A=\frac{1}{2}\times base\times height$.
$A=\frac{1}{2}\times2\times6 = 6$.
# Answer: 6

### Question 16: What is the perimeter of parallelogram AEDC?
# Explanation:
## Step1: Recall that in a parallelogram, opposite sides are equal. So we need to find the lengths of AE and ED (or DC and AE, etc.).
- Length of AE: From question 13, AE = $2\sqrt{10}$ (or approximately 6.32).
- Length of ED: Coordinates of E(-2, -3) and D(4, -3). Horizontal line, so length is $|4 - (-2)| = 6$.
## Step2: Use the perimeter formula for a parallelogram $P = 2\times(side1 + side2)$.
$P = 2\times(2\sqrt{10}+6)=4\sqrt{10}+12$ (or approximately $4\times3.16 + 12 = 12.64+12 = 24.64$).
# Answer: $12 + 4\sqrt{10}$ (or approximately 24.64)

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QUESTION IMAGE

Question

Explanation:

Question 10: How many sides does the polygon AFDCB have?

Step1: Identify the vertices of the polygon AFDCB.

Step2: Count the number of vertices (which equals the number of sides in a polygon).

Step1: Identify the coordinates of A and F.

Step2: Use the distance formula for vertical lines (since x - coordinates are the same).

Answer:

Question 11: Is it concave or convex?